Centripetal acceleration for a polyline Given a polyline (x and y coordinates) in Cartesian coordinate system and time component, how can I estimate centripetal acceleration (let's say an average one)? (I have a list of  pairs. Each pair  was measured at 1 minute interval. So, from this information, I can easily estimate speed and acceleration.)
I know that the centripetal acceleration it is the rate of change of tangential velocity. But the problem is that tangential velocity formula involves the radius of circular path, and my path (polyline) just has some curvatures. So, I don't know how to get the radius.
As a starting point, I think that it's necessary to estimate angles using these formulas: 
radian = math.atan2((y2 - y1),(x2 - x1))
degrees = radian * 180 / math.pi

But I don't know how to proceed from it. Do I need to estimate all angles between sequential  points and then integrate these angles over time...?
Any clarification is highly appreciated.

 A: Actually, you must have a $\textbf{r}(t)$ function. Your polyline can be probably considered as one. If you want constant speed, maybe you will have problems.
The curvature of a such curve can be expressed by the formula $\kappa=\frac{|\dot{\textbf{r}}\times \ddot{\textbf{r}}|}{|\dot{\textbf{r}}^3|}$. Its recipe is radius, which can be substituted into the formula of the centrifugal acceleration of the circular movement ($\textbf{a}=\frac{v^2}{R}$).
A: For numerical safety, I recommend to use the Savitzky-Golay filters for derivation.
Use them to compute the first and second derivatives of the coordinates over time.
The speed vector is $\vec v=(\dot x(t),\dot y(t))$. The acceleration vector is $\vec a=(\ddot x(t),\ddot y(t))$.
The centripetal acceleration is the component of the acceleration orthogonal to the trajectory, i.e. orthogonal to the speed vector. It is given by
$$a_c=||\vec a\times\frac{\vec v}v||.$$
Similarly, the tangential acceleration is given by the projection on the tangent,
$$a_t=\vec a\cdot\frac{\vec v}v.$$
